Chapter 18 Data Analysis Overview Yandell – Econ 216 Chap 18-1

Learning Objectives In this chapter, you learn: The steps involved in choosing what statistical methods to use to conduct a data analysis Yandell – Econ 216 Chap 18-2

Good Data Analysis Requires Choosing The Proper Technique(s) Choosing the proper technique(s) to use requires the consideration of: The purpose of the analysis The type of variable being analyzed Numerical Categorical The assumptions about the variable you are willing to make Yandell – Econ 216 Chap 18-3

Questions To Ask When Analyzing Numerical Variables Do you seek to: Describe the characteristics of the variable (possibly broken into several groups) Draw conclusions about the mean and standard deviation of the variable in a population Determine whether the mean and standard deviation of the variable differs depending on the group Determine which factors affect the value of the variable Predict the value of the variable based on the value of other variables Determine whether the values of the variable are stable over time Yandell – Econ 216 Chap 18-4

How to Describe the Characteristics of a Numerical Variable Develop tables and charts and compute descriptive statistics to describe the variable’s characteristics: Tables and charts Stem-and-leaf display, percentage distribution, histogram, polygon, boxplot, normal probability plot Statistics Mean, median, mode, quartiles, range, interquartile range, standard deviation, variance, and coefficient of variation Yandell – Econ 216 Chap 18-5

How to draw conclusions about the population mean or standard deviation Confidence interval for the mean based on the t-distribution Hypothesis test for the mean (t-test) Yandell – Econ 216 Chap 18-6

How to determine whether the mean or standard deviation differs by group Two independent groups studying central tendency Normally distributed numerical variables Pooled t-test if you can assume variances are equal Separate-variance t-test if you cannot assume variances are equal Both tests assume the variables are normally distributed and you can examine this assumption by developing boxplots and normal probability plots To decide if the variances are equal you can conduct an F- test for the ratio of two variances Numerical variables not normally distributed Wilcoxon rank sum test Yandell – Econ 216 Chap 18-7

How to determine whether the mean or standard deviation differs by group Two groups of matched items or repeated measures studying central tendency Paired differences normally distributed Paired t-test Two independent groups studying variability Numerical variables normally distributed F-test continued Yandell – Econ 216 Chap 18-8

Three or more independent groups and studying central tendency Numerical variables normally distributed One Way Analysis of Variance Numerical variables not normally distributed Kruskal-Wallis Rank Test continued Yandell – Econ 216 Chap 18-9 How to determine whether the mean or standard deviation differs by group

How to determine which factors affect the value of the variable Two factors to be examined Two-factor factorial design Yandell – Econ 216 Chap 18-10

How to predict the value of a variable based on the value of other variables One independent variable Simple linear regression model Two or more independent variables Multiple regression model Data taken over a period of time and you want to forecast future time periods Moving averages Exponential smoothing Least-squares forecasting Autoregressive modeling Yandell – Econ 216 Chap 18-11

How to determine whether the values of a variable are stable over time Studying a process and have collected data over time Develop R and charts Yandell – Econ

Questions To Ask When Analyzing Categorical Variables Do you seek to: Describe the proportion of items of interest in each category (possibly broken into several groups) Draw conclusions about the proportion of items of interest in a population Determine whether the proportion of items of interest differs depending on the group Predict the proportion of items of interest based on the value of other variables Determine whether the proportion of items of interest is stable over time Yandell – Econ 216 Chap 18-13

How to describe the proportion of items of interest in each category Summary tables Charts Bar chart Pie chart Pareto chart Side-by-side bar charts Yandell – Econ 216 Chap 18-14

How to draw conclusions about the proportion of items of interest Confidence interval for proportion of items of interest Hypothesis test for the proportion of items of interest (Z-test) Yandell – Econ 216 Chap 18-15

How to determine whether the proportion of items of interest differs depending on the group Categorical variable has two categories Two independent groups Two proportion Z-test for the difference between two proportions Two groups of matched or repeated measurements McNemar test More than two independent groups for the difference among several proportions More than two categories and more than two groups of independence    test Yandell – Econ 216 Chap 18-16

How to determine whether the proportion of items of interest is stable over time Studying a process and data is taken over time Collected items of interest over time p-chart Yandell – Econ 216 Chap 18-17

Data Analysis Tree Numerical & Categorical Variables Numerical Variables Categorical Variables Possible Questions How to describe the characteristics of the variable (possibly broken into several groups)? How to draw conclusions about the mean and standard deviation of the variable in the population? How to determine whether the mean and standard deviation of the variable differs depending on the group? How to determine which factors affect the value of the variable? How to predict the value of the variable based on the value of other variables? How to determine whether the values of the variable are stable over time? How to describe the proportion of items of interest in each category (possibly broken into several groups)? How to draw conclusions about the proportion of items of interest in a population? How to determine whether the proportion of items of interest differs depending on the group? How to predict the proportion of items of interest based on the value of other variables? How to determine whether the proportion of items of interest is stable over time? Yandell – Econ 216 Chap 18-18

Data Analysis Tree Numerical Variables How to describe the characteristics of the variable (possibly broken into several groups)? How to draw conclusions about the mean and standard deviation of the variable in the population? How to determine whether the mean and standard deviation of the variable differs depending on the group? continued Create Tables & Charts Calculate Statistics Mean Variance Stem-and-leaf display, percentage distribution, histogram, polygon, boxplot, normal probability plot Mean, median, mode, quartiles, range, interquartile range, standard deviation, variance, coefficient of variation Confidence interval for mean (t or z) Hypothesis test for mean (t or z) Pooled t test (both variables must be normal, variances equal) Separate variance t test ( both variables must be normal) Wilcoxon rank sum test ( variables do not have to be normal) F-test ( both variables must be normal) Paired t test (differences must be normal) One Way Anova (variable must be normal) Kruskal-Wallis Rank Test (variable doesn’t need to be normal) 2 independent groups 2 matched groups >2 independent groups Yandell – Econ 216 Chap 18-19

Data Analysis Tree Numerical Variables continued How to determine which factors affect the value of the variable? How to predict the value of the variable based on the value of other variables? How to determine whether the values of the variable are stable over time? Two factors to be examined One independent variable Two or more Independent variables Data taken over time to forecast the future Studied a process and taken data over time Two factor factorial design Simple linear regression Multiple regression model Moving averages Exponential smoothing Least squares forecasting Autoregressive modeling Develop and R charts Yandell – Econ 216 Chap 18-20

Data Analysis Tree Categorical Variables continued How to describe the proportion of items of interest in each category (possibly broken into several groups) How to draw conclusions about the proportion of items of interest in a population How to determine whether the proportion of items of interest differs depending on the group Summary tables Bar charts Pie charts Pareto charts Side-by-side charts Confidence interval for the proportion of items of interest Hypothesis test for the proportion of items of interest Two proportion Z test test for the difference between two proportions McNemar test test for the difference among several proportions test of independence Two categories & two independent groups Two categories & two matched groups Two categories & more than two independent groups More than two categories & more than two groups Yandell – Econ 216 Chap 18-21

How to determine whether the proportion of items of interest is stable over time continued p-chart Studying a process and collected items of interest over time Yandell – Econ 216 Chap Data Analysis Tree Categorical Variables

Chapter Summary Discussed how to choose the appropriate technique(s) for data analysis for both numerical and categorical variables Discussed potential questions and the associated appropriate techniques for numerical variables Discussed potential questions and the associated appropriate techniques for categorical variables Yandell – Econ 216 Chap 18-23